Large-Dimensional Replicator Equations with Antisymmetric Random Interactions

抄録

We study the asymptotic behavior of effective degrees of freedom (i.e., the number of species or the diversity) of large-dimensional replicator equations (RE) with quenched antisymmetric random interspecies interactions. It is found that the diversity is maintained at the order of initial diversity N if the random interactions are antisymmetric, while it is known that the diversity rapidly decreases to order 1 via “extinction” in the RE with symmetric or asymmetric random quenched interactions. In the antisymmetric case, the global stability of a unique attracting set is contrasted to the symmetric and asymmetric cases which have many attractors in general. The present result suggests a new mechanism of maintaining biodiversity which resolves the “paradox of ecology”.